weakBruhatOrder(w,v)
The (right) weak Bruhat order is a partial order on the symmetric group $\mathfrak{S}_n$. For two permutations $p$ and $q$, $w \leq_R v$ if and only if $\ell(w) + \ell(v^{-1} w) = \ell(v)$, where $\ell$ denotes the length(Permutation) of a permutation and $\leq_R$ is the right weak Bruhat order. See [BB05] for more details on the weak Bruhat order.
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By default, weakBruhatOrder computes the right weak Bruhat order, but the optional argument {tt Side} can be used to compute, for example, the left weak Bruhat order. The current options for Side are "left" and "right".
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The object weakBruhatOrder is a method function with options.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Permutations/Documentation/mainDocs.m2:850:0.